What did Galois determine about polynomials in his teens?
Insufficient condition for quadratics
Necessary and sufficient condition for solvability by radicals
A theory for complex number polynomials
Method for integration of polynomials
Answer
Galois' pivotal discovery in his teenage years was the necessary and sufficient condition for a polynomial to be solvable by radicals. This groundbreaking work provided a profound understanding of the solvability of equations, fundamentally transforming the field of mathematics. Galois' revolutionary insights laid the groundwork for modern algebra and continue to inspire mathematicians to this day.
Gallant Galois: The Life and Legacy of a French Mathematician
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